PROBING into Man Haron Monis's online life has revealed no links to the Islamic State, despite his claim to be working for the terror group during the Lindt Cafe siege in Sydney.

A coronial inquest heard from several mental health workers with differing assessments of Monis's state of mind, ranging from no mental illness to delusional schizophrenia.

Psychologist Kasim Abaie, who saw Monis three times in 2010, said the gunman believed he was being followed by ASIO and "people could read his mind".

The inquest was shown an email from Monis inviting Prime Minister Tony Abbott to a "live debate" and YouTube clips of him delivering lectures. But Detective Senior Constable Murray Northey, who spent months digging through Monis's internet trail, said there was no evidence of links to IS.